Problem: Calculate the quotient below and give your answer in scientific notation. ${\dfrac{180}{9\times 10^{-5}}} =\ ?$
Solution: First, let's change the number in the numerator into scientific notation. ${\dfrac{180}{9.0\times 10^{-5}}} = {\dfrac{1.80\times 10^{2}}{9.0\times 10^{-5}}} $ Start by collecting the significands and exponents. $ {\dfrac {{1.80} \times {10^{2}}} {{9.0} \times {10^{-5}}} = {\dfrac{1.80}{9.0}} \times {\dfrac{10^{2}}{10^{-5}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.20} \times {10^{2 \,-\, -5}}$ $= {0.20} \times {10^{7}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.20}$ is the same as ${2.0 \div 10}$, or ${2.0 \times 10^{-1}}$. $ = {2.0 \times 10^{-1}} \times {10^{7}} $ $ = 2.0 \times 10^{{-1} + {7}} $ $= 2.0\times 10^{6}$